Cartographers often use Euclidean maps to illustrate the measurement of an underlying statistical or thematic variable across a geographical area, usually by shading the Euclidean map according to a shading scale corresponding to the measured value of the underlying variable. The shading scale is usually chosen as a progression from a light shade to a darker shade to show the level of the variable as it increases, and the shading is applied to regions of the map according to the average value of the thematic variable in that particular region. Maps shaded in this way are also known as choropleth maps, any they provide a way to visualize the measurement of a variable across a geographic area or to show the variability of the measurement within the region.
Choropleth maps are increasingly common in the field of communicating and interpreting epidemiological or health data due to the use of cartography software. However, it may be difficult for the viewer of a choropleth map to understand certain aspects of the presented data, especially under certain conditions relating to the distribution of the demographic variable. For example, if the demographic variable is not distributed evenly across the map, it is difficult to recognize the magnitude of the measurement and interpret the results because a large accumulation of data points could potentially be represented by a relatively small amount of space on the map. An example is a map illustrating a sampling of a per capita characteristic of persons over a country, such as household income, where low population areas contain far fewer individuals than urban areas, and thus a large fraction of the population will be represented on only a small fraction of the map surface, i.e., the higher density urban areas. The low population areas tend to dominate these maps when applied to typical real-world land use patterns. Viewers of Euclidean choropleths may fail to recognize this, especially if they are unfamiliar with the geography and density of the geographic area.
To provide a more intuitive presentation of thematic data over a geographical area, cartograms may be substituted for Euclidean choropleths. Cartograms are made by a technique wherein a demographic mapping variable substitutes for land area as normally shown on an Euclidean map. A cartogram distorts the surface of the Euclidean map to depict a zone's area on the map as proportional to the level of the demographic variable contained therein. Cartograms therefore do not depict actual geographic space. Cartogram zones may include anything that exists in geographic space such as a country, state, city, county, borough, town, river, mountain range, etc. Common types of cartograms include distance cartograms, which are distorted to show travel time between points, and value-by-area cartograms, which are distorted to show the prevalence of a characteristic that varies according to location on a map, usually a demographic characteristic such as population, votes for a candidate, number of patents filed, number of automobiles owned, gross domestic product, educational level, etc. When a value-by-area cartogram is based on population, it is often termed an isodemographic map. In this way, an isodemographic map would illustrate the relative sizes of the populations of real-world areas by scaling the area allotted to each according to its population rather than to its physical geographical area in the conventional manner. For example, if a region accounts for 20% of the population of a country, it will occupy 20% of the surface area on an isodemographic cartogram of that country.
Euclidean maps may be distorted to create cartograms according to a number of known algorithms that may differ in their effects on the map's continuity, shape preservation, orientation, and topology preservation relative to the Euclidean map. For example, a cartogram distortion algorithm that forces neighboring map features to maintain their borders regardless of the distorted size of the features is known as a contiguous cartogram. In a contiguous cartogram, the topology between objects is maintained, but, as a group, the objects may lose their shape, giving the cartogram a “pinched” appearance, depending on the amount of distortion. Contiguous cartograms may render the depicted geographical area unrecognizable to a viewer if there are physical geographical areas that have little or no measurement of the underlying thematic variable. For example, contiguous isodemographic cartograms appear to omit low population areas that occupy large amounts of geographic space, such as a desert or mountain region.
A non-contiguous cartogram, on the other hand, does maintain connectivity between adjacent features, but instead allows the features to grow or shrink in size and still maintain their familiar shape. Non-contiguous cartograms may, instead of enlarging or shrinking map objects, replace them with objects of a uniform shape such as, for example, a circle or vertical bar. Shapes in a non-contiguous cartogram often do not overlap, but rather are rearranged so that the full area of each shape can be seen.
Each of these existing cartogram rendering methods provides a different visual appearance of the data, and may be more or less suitable for communicating and interpreting underlying data depending on the data's distribution. These cartogram rendering methods, however, suffer from a drawback that impairs the presentation of the underlying data. In these cartograms, shaded zones are based on administrative boundaries representing arbitrary borders or borders that do not align with population patterns such as towns, boroughs, counties, cities, regions, states, territories, or other ad-hoc groupings such as those based on industry criteria. These zones may introduce abrupt transitions in the shading pattern of the map due to issues such as meshing or border effects. Meshing effects are due to the variations in size of geographical zones, especially towns and cities; border effects result in variables that can seem to have major differences between two neighboring zones even though the variables likely change smoothly and continuously over the area in reality. Adjusting the size of zones does not provide a satisfactory solution to the problem. On one hand, if the zones are chosen to be small units to obtain good geographical accuracy and avoid the meshing and border effects, the map will take on an inlaid effect that will make it difficult for the viewer to read and interpret. On the other hand, if the zones are enlarged, then the map will be easy for the viewer to read, but will diminish accuracy and a reduce resolution of information conveyed to the viewer.